1. Field of the Invention
The invention relates generally to optical waveguide rotation sensors, and especially to apparatus and methods of measuring the rotation-induced phase shift between light waves counterpropagating in the closed path of a Sagnac interferometer to determine rate of rotation.
2. Description to the Related Art
An optical interferometer used for rotation sensing and measurement generally comprises a coherent source of light, a closed optical path, means for coupling light from the source into and out of the closed path, and means for detecting and processing the optical interference signal coming from the closed path.
There are two types of disturbances in an optical path that can give rise to phase shifts in light waves traveling in opposite directions around a closed optical path: reciprocal and non-reciprocal. A reciprocal disturbance is one that affects either light wave in a similar manner despite the fact that the two waves are traveling in different directions and may be subjected to the disturbance at different times. A non-reciprocal disturbance affects the two waves differently, either because it occurs over a time interval comparable to the time it takes a wave to travel around the closed path, or because the effect it has on a wave depends on the direction of propagation of the wave around the closed path.
The Sagnac effect, a relativistic physical phenomenon, is a non-reciprocal effect in which the rotation of a closed optical path causes light waves propagating in opposite directions along the path to take different amounts of time to complete a transit of the closed path. This difference in transit time results in a phase difference between the two light waves proportional to rotation rate. When the beams are recombined on a photodetector, they give rise to an interference pattern which is a function of the non-reciprocal phase shift. Measurement of the phase difference is a measure of the rate of rotation of the optical path.
If .phi..sub.S denotes the Sagnac phase difference between the recombined counterpropagating light beams, the intensity of light due to the interfering beams varies as cos(.phi..sub.S). When the phase difference is close to zero, the cosine function varies only slightly with changes in phase difference. In addition, it is impossible to determine the sign of the phase shift from the intensity variation. In order to increase the sensitivity of detection, it is advantageous to introduce artificially an added fixed phase shift or "bias" to shift to a point of operation on the cosine curve where the rate of change of intensity with respect to .phi..sub.S is greater. In particular, maximum sensitivity and linearity of response are achieved by introducing a non-reciprocal phase bias such as .pi./2 radians. At this point, the light intensity is proportional to cos(.phi..sub.S +.pi./2)=sin (.phi..sub.S). The periodic nature of the cosine function results in an equivalent maximum sensitivity and linearity of response (apart from algebraic sign) at any odd integral multiple of plus or minus .pi./2.
It has proven difficult to a construct a device for introducing a non-reciprocal phase bias which is sufficiently stable. However, non-reciprocal phase shifts may be temporarily induced by a reciprocal phase modulator placed near one end of the optical circuit.
A phase modulator device can be based, for example, on the change in refractive index with applied voltage in an electro-optic crystal forming part of the closed optical path of the interferometer. If the phase modulator is placed near one end of the fiber coil, application of a voltage to the modulator produces a modulation of the phase of one of the counterpropagating waves entering the loop that is not experienced by the other until it has traveled all the way around the coil. The second wave experiences a phase modulation which is delayed by the length of time required for light to propagate around the coil, a time given by EQU .tau..sub.o =nL/c,
where n is the index of refraction of the fiber material, L is the length of the fiber coil, and c is the speed of light in vacuum. If V(t) is a time-varying signal applied to the phase modulator, the phase difference between the counterpropagating light waves is proportional to V(t)-V(t-.tau..sub.o). In this way a phase bias can be produced which sets the operating point of the interferometer.
If there is a rotation of the fiber coil, a phase shift .phi..sub.S will be added to the phase bias due to the non-reciprocal nature of the Sagnac effect. Although it is possible to use the output signal of the photodetector to estimate the rotation directly, it is preferable to use a "nulling" or "zeroing" method and to estimate the rotation from a feedback modulation signal, in order to avoid linearity errors resulting from the intensity interference function. The idea is to generate a feedback modulation signal which introduces a non-reciprocal phase shift in the optical circuit which is equal in magnitude but opposite in sign to the rotationally-induced phase shift, thereby "nulling" or "zeroing" the variation of the intensity signal. Application of the feedback modulation signal to the phase modulator produces a phase difference between the counterpropagating waves which is continuously equal and opposite in sign compared to the phase shift induced by the rotation of the closed optical path. A method such as this in which there is a closed feedback loop is often referred to as a "closed-loop" method.
One method of closed-loop feedback, generally known as the "serrodyne method," makes use of a feedback modulation signal which is a reciprocal phase ramp having a slope proportional to .phi..sub.S /.tau..sub.o, where .phi..sub.S is a constant rotationally-induced phase shift and .tau..sub.o is the time taken for a light wave to travel around the closed light path of the interferometer in the absence of any rotation. A bias modulation signal consists of a voltage square-wave having an amplitude which induces a phase shift of plus or minus .pi./2 radians and a frequency equal to 1/2.tau..sub.o. Since the reciprocal phase ramp signal cannot increase indefinitely, the serrodyne method actually generates a sawtooth feedback waveform with a peak-to-peak amplitude of 2.pi. radians, with the 2.pi. phase transition effectively resetting the operating point of the interferometer to an equivalent position on the intensity interference curve relating output signal to input phase difference.
U.S. Pat. No. 4,705,399 to Graindorge et al, entitled "Device for Measuring a Non-reciprocal Phase Shift Produced in a Closed-Loop Interferometer," discloses a serrodyne phase modulation method in which a digital phase ramp in the form of a staircase-shaped voltage feedback signal is combined with a bias modulation signal of the type described above. The digital staircase signal consists of a sequence of voltage steps, each of duration .tau..sub.o, to the phase modulator. In general, the amplitude of each step change is calculated to provide a non-reciprocal phase shift of plus or minus .pi./2 radians minus a Sagnac phase estimate. The intensity output of the interferometer is demodulated at the bias modulation frequency, namely 1/2.tau..sub.o.
The resulting signal is proportional to the residual Sagnac phase shift. It is this signal that a closed-loop controller will act to "null" or "zero." To avoid problems with voltage saturation, the modulation steps are occasionally required to "roll over" in the phase bias resetting operation described above. The step voltage to the phase modulator is adjusted to provide an additional phase shift of plus or minus 2.pi. radians to keep the voltage to the phase modulator in a reasonable operating range. Additional demodulation logic may be employed during these roll-overs to determine the error in estimated phase modulator gain. Through subsequent roll-overs, the estimated phase modulator gain error may be nulled. The phase modulator gain is the proportionality constant relating the phase induced by the phase modulator in response to a given value of input voltage. This secondary loop control, as it is formally known, provides additional scale factor stability to the sensor. The scale factor for a closed-loop rotation sensing interferometer is proportional to the product of the Sagnac scale factor and the phase modulator gain. The Sagnac scale factor is the constant of proportionality between rate of rotation and the Sagnac phase shift.
Another phase modulation method which can be used is direct digital feedback, which is also a closed-loop method. Such a method is disclosed in U.S. patent application Ser. No. 031,323, entitled "Rotation Rate Nulling Servo and Method for Fiber-optic Rotation Sensor," by Jim Steele, filed Mar. 27, 1987, and assigned to the assignee of the present invention. The application by Steele is hereby incorporated by reference in the present application.
The Steele application discloses a direct digital feedback circuit which operates by alternately presetting the voltage drive on the phase modulator to zero and waiting for at least one transit time .tau..sub.o for the applied phase to go reciprocal, then switching the phase modulator voltage to a level corresponding to a non-reciprocal phase shift which is the difference between a reference (-3.pi./2, -.pi./2, +.pi./2, +3.pi./2 radians) and the Sagnac phase estimate. The resulting intensity signal is gated and observed for one transit time .tau..sub.o immediately following the setting of the reference voltage. The process is repeated in a predetermined sequence of reference levels and the results are processed to continuously develop a Sagnac phase estimate and a phase modulator gain estimate (secondary control) with which to adjust the amplitudes of the voltages to the phase modulator.
The major disadvantages of digital serrodyne methods are hardware complexity and cost in the case of short (less than 200 m) fiber length coils. The digital serrodyne method requires high effective processing rates (1/.tau..sub.o Hz) in order to generate the feedback terms, calculate roll-over, and drive the phase modulator. In addition, the use of shorter-length fiber coils begins to necessitate multiple D/A converters for modulation, since typical state-of-the-art D/A converters have inadequate settling times. Direct digital feedback may be implemented in short-length fiber coils in a hardware-efficient manner; however, the direct digital feedback method is susceptible to bias errors due to phase shifts in the detection circuitry and intensity modulation effects in the phase modulator.